ORCID Profile
0000-0002-9859-100X
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Publisher: Cambridge University Press (CUP)
Date: 09-11-2020
DOI: 10.1017/S0004972720001215
Abstract: For an infinite Toeplitz matrix T with nonnegative real entries we find the conditions under which the equation $\\boldsymbol {x}=T\\boldsymbol {x}$ , where $\\boldsymbol {x}$ is an infinite vector column, has a nontrivial bounded positive solution. The problem studied in this paper is associated with the asymptotic behaviour of convolution-type recurrence relations and can be applied to problems arising in the theory of stochastic processes and other areas.
Publisher: Cambridge University Press (CUP)
Date: 2007
DOI: 10.1017/S1446181100003503
Abstract: The interest in retrial queueing systems mainly lies in their application to telephone systems. This paper studies multiserver retrial queueing systems with n servers. The arrival process is a quite general point process. An arriving customer occupies one of the free servers. If upon arrival all servers are busy, then the customer waits for his service in orbit, and after a random time retries in order to occupy a server. The orbit has one waiting space only, and an arriving customer, who finds all servers busy and the waiting space occupied, is lost from the system. Time intervals between possible retrials are assumed to have arbitrary distribution (the retrial scheme is explained more precisely in the paper). The paper provides analysis of this system. Specifically the paper studies the optimal number of servers to decrease the loss proportion to a given value. The representation obtained for the loss proportion enables us to solve the problem numerically. The algorithm for numerical solution includes effective simulation, which meets the challenge of a rare events problem in simulation.
Publisher: Springer Science and Business Media LLC
Date: 05-2008
Publisher: Cambridge University Press (CUP)
Date: 03-2001
DOI: 10.1017/S0021900200018635
Abstract: The present paper provides simple inequalities for the number of lost customers during a busy period of a GI / M /1/ n queueing system.
Publisher: Cambridge University Press (CUP)
Date: 09-1997
DOI: 10.1017/S0021900200101469
Abstract: This paper consists of two parts. The first part provides a more elementary proof of the asymptotic theorem of the refusals stream for an M/GI/ 1 /n queueing system discussed in Abramov (1991a). The central property of the refusals stream discussed in the second part of this paper is that, if the expectations of interarrival and service time of an M/GI/ 1 /n queueing system are equal to each other, then the expectation of the number of refusals during a busy period is equal to 1. This property is extended for a wide family of single-server queueing systems with refusals including, for ex le, queueing systems with bounded waiting time.
Publisher: Springer Science and Business Media LLC
Date: 30-11-2007
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 11-2012
Publisher: Informa UK Limited
Date: 27-11-2018
Publisher: Cambridge University Press (CUP)
Date: 12-2001
Publisher: The Optical Society
Date: 29-03-2013
Publisher: Springer Science and Business Media LLC
Date: 2001
Publisher: MDPI AG
Date: 07-01-2023
Abstract: The single point insulin sensitivity estimator (SPISE) is a recently developed fasting index for insulin sensitivity based on triglycerides, high density lipoprotein cholesterol, and body mass index. SPISE has been validated in juveniles and adults still, its role during childhood remains unclear. To evaluate the age- and sex-specific distribution of SPISE, its correlation with established fasting indexes and its application as a prognostic marker for future dysglycemia during childhood and adolescence were assessed. We performed linear modeling and correlation analyses on a cross-sectional cohort of 2107 children and adolescents (age 5 to 18.4 years) with overweight or obesity. Furthermore, survival analyses were conducted upon a longitudinal cohort of 591 children with overweight/obesity (1712 observations) with a maximum follow-up time of nearly 20 years, targeting prediabetes/dysglycemia as the end point. The SPISE index decreased significantly with age (−0.34 units per year, p 0.001) among children and adolescents with overweight and obesity. Sex did not have an influence on SPISE. There was a modest correlation between SPISE and established fasting markers of insulin resistance (R = −0.49 for HOMA-IR, R = −0.55 for QUICKI-IR). SPISE is a better prognostic marker for future dysglycemia (hazard ratio (HR) 3.47, 95% confidence interval (CI) 1.60–7.51, p 0.01) than HOMA-IR and QUICKI-IR (HR 2.44, 95% CI 1.24–4.81, p 0.05). The SPISE index is a surrogate marker for insulin resistance predicting emerging dysglycemia in children with overweight or obesity, and could, therefore, be applied to pediatric cohorts that lack direct insulin assessment.
Publisher: Springer Science and Business Media LLC
Date: 22-10-2008
Publisher: Cambridge University Press (CUP)
Date: 23-06-2023
DOI: 10.1017/S0004972723000539
Abstract: We derive conditions for recurrence and transience for time-inhomogeneous birth-and-death processes considered as random walks with positively biased drifts. We establish a general result, from which the earlier known particular results by Menshikov and Volkov [‘Urn-related random walk with drift $\\rho x^\\alpha /t^\\beta $ ’, Electron. J. Probab. 13 (2008), 944–960] follow.
Publisher: Informa UK Limited
Date: 2007
Publisher: Springer Science and Business Media LLC
Date: 09-2004
Publisher: Cambridge University Press (CUP)
Date: 09-1994
DOI: 10.2307/3215141
Abstract: This paper considers the asymptotic distribution of the maximum number of infectives in an epidemic model by showing that, as the initial number of susceptibles converges to infinity, the process of infectives converges almost surely to a birth and death process. The model studied here is more general than usual (see e.g. Bailey (1975), Bharucha-Reid (1960), Keilson (1979)) in that it incorporates immigration and the limiting birth and death process is non-linear. The main novelty of the present paper is the martingale approach used to prove the above-mentioned convergence.
Publisher: Informa UK Limited
Date: 12-2006
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 2019
Publisher: Springer Science and Business Media LLC
Date: 19-11-2018
Publisher: Elsevier BV
Date: 09-2002
Publisher: Springer Science and Business Media LLC
Date: 2002
Publisher: National Library of Serbia
Date: 2022
DOI: 10.2298/PIM2225041A
Abstract: We provide numerical procedures for possibly best evaluating the sum of positive series under quite general setting. Our procedures are based on the application of a generalized version of Kummer's test.
Publisher: Elsevier BV
Date: 03-2013
Publisher: National Library of Serbia
Date: 2021
DOI: 10.2298/PIM2123061A
Abstract: The paper provides a new test of convergence and ergence of positive series. In particular, it extends the known test by Margaret Martin [Bull. Amer. Math. Soc. 47 (1941), 452-457].
Publisher: Informa UK Limited
Date: 23-04-2020
Publisher: Springer Science and Business Media LLC
Date: 2000
Publisher: Springer Science and Business Media LLC
Date: 2006
Publisher: Springer Science and Business Media LLC
Date: 15-07-2010
Publisher: Springer Science and Business Media LLC
Date: 16-06-2012
Publisher: Informa UK Limited
Date: 31-10-2008
Publisher: Springer Science and Business Media LLC
Date: 27-02-2017
Publisher: Springer Science and Business Media LLC
Date: 03-2004
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2004
Publisher: Cambridge University Press (CUP)
Date: 03-2007
DOI: 10.1017/S0021900200002849
Abstract: A large dam model is the object of study of this paper. The parameters L lower and L upper define its lower and upper levels, L = L upper - L lower is large, and if the current level of water is between these bounds, the dam is assumed to be in a normal state. Passage across one or other of the levels leads to damage. Let J 1 and J 2 denote the damage costs of crossing the lower and, respectively, the upper levels. It is assumed that the input stream of water is described by a Poisson process, while the output stream is state dependent. Let L t denote the dam level at time t , and let p 1 = lim t →∞ P{ L t = L lower } and p 2 = lim t →∞ P{ L t & L upper } exist. The long-run average cost, J = p 1 J 1 + p 2 J 2 , is a performance measure. The aim of the paper is to choose the parameter controlling the output stream so as to minimize J .
Publisher: Element d.o.o.
Date: 2022
Publisher: American Institute of Mathematical Sciences (AIMS)
Date: 2011
Publisher: Springer Science and Business Media LLC
Date: 15-02-2023
Start Date: 2007
End Date: 2009
Funder: Australian Research Council
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